What is the limit as x approaches-1+of (x+1)/(|x+1|) ?

The limit as x approaches-1+of (x+1)/(|x+1|) is 1

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limit as x approaches-1+of (x+1)/(|x+1|)

x \to - 1 + lim (\frac{x + 1}{∣ x + 1 ∣})

1

Solution steps

x \to - 1 + lim (\frac{x + 1}{∣ x + 1 ∣})

x + 1

is positive when

x \to - 1 +

. Therefore

∣ x + 1 ∣ = x + 1

= x \to - 1 + lim (\frac{x + 1}{x + 1})

Simplify

= x \to - 1 + lim (1)

x \to a lim c = c

= 1

What is the limit as x approaches-1+of (x+1)/(|x+1|) ?
The limit as x approaches-1+of (x+1)/(|x+1|) is 1